Acceleration is pretty normal when push the pedal once on that morning but when performing it again moments later the accelaration is very slow and the rpm would never reach to 3000, and when steady, its below 1000rpm, somewhere about 600-700rpm, l would not be able to overtake cause of this problem and goes slower in summer including pushing the whole pedal down and stop and start from hill.
So it is like l can only use a good accelaration once and after then, it starts to go slow and sometimes when parked l can smell the funny rubber smell from the hood.

l have had it fix (BM specialist) from diagnosis, fixing the break pads, servicing, oil leaks and change head gasket. From all this, the car performance improved but not as normal as it should be. It cost me way more than just a 4 digit charge and im still stuck at this. Any suggestion about this information regarding to any of this would be helpful. Thanking you.

BM 316 '95 model, automatic, 115,000k

if l was you l would get the car put on a bmw diagnostic computer.to me it sounds like the computer has been put in limp home mode which would cause all your problems

ljtarano could be right,check that out.
b4 u go for diagnostic test,pls check following,
1) CHECK FOR VACUUM LEAKS.
2) CHECK IF VACUUM HOSES FITTED WRONGLY,
3)CHECK FUEL PUMP AND FILTER.
4)CHECK THE BRAKES ,IT COULD BE JAMMING UP.
5)HAVE THE HOSE TO BRAKE BOOSTER PUMP CHECKED FOR LEAKS OR ONE WAY VALVE IS FACING WRONG DIRECTION.
6)CHECK THE T NEXT TO INLET MANIFOLD,AT TIMES THE HOSES SLIP OUT, AND U MAY NOT KNOW.U MAY THINK IS IN PLACE,BUT THE LEAK COULD BE FROM THERE.
7)CHECK THE HT WIRES TO SPARK PLUG,ONE COULD BE IN WRONG PLACE.
WISH U LUCK.

My best mate is a service tech at BMW Sydney. But because l can not understand your question, lacking as it does sentences and punctuation, l can not help.

Believe it or not - if you have the original catalytic converter - that is your problem.

l can guess, & give u a long list of possibilities, but that is not the way BMW is r diagnosed or repaired.
You would waste a lot of time, money & incur loads of aggravation & frustration by guessing.
My recommendation is to change ur mechanic, go to a real
BMW mechanic who has training, experience & the right diagnostic tools.
But if u have the time, try looking at the accelerator cable & its linkage to the throttle valve (while somebody else is pressing the accelerator pedal up & down). See if the bowden cable is functioning properly, perhaps it is loosely attached or the inside cable does not move freely.
Check fuel pressure at the fuel rail, perhaps u have a defective fuel pump or clogged filter.
Check for vacuum leaks. Verify that all the vacuum hoses r properly attached & in good condition. Perhaps the idle air valve (the small round thing connected to the throttle valve) is bad.
The funny rubbery smell is perhaps the most important clue that u have given. So use ur nose & eyes to verify where it is coming from (stuck brake pads, melting hoses, melting wires, etc.).
You never mentioned the idle characteristics of ur engine, same thing with presence of misfires, so these r all that l can say (my ''guesses'').

l had the same problem, but l do not remember what l did.
you might wanna ask real bmw fanatics
http://bimmerforums.com/